Mathematics 9709/42 — October/November 2013

A small block of weight $5.1\text{ N}$ rests on a smooth plane inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac{8}{17}$. The block is held in equilibrium by means of a light inextensible string. The string makes an angle $\beta$ above the line of greatest slope on which the block rests, where $\sin \beta = \frac{7}{25}$ (see diagram). Find the tension in the string.